Abstract: A new approach to harmonic analysis on the unit sphere in is given, closer in form to Fourier analysis on than the usual development in orthonormal polynomials. Singular integrals occur in the transform formulae. The results generalize to symmetric space.

[4]E.
T. Whittaker and G.
N. Watson, A course of modern analysis, Cambridge Mathematical
Library, Cambridge University Press, Cambridge, 1996. An introduction to
the general theory of infinite processes and of analytic functions; with an
account of the principal transcendental functions; Reprint of the fourth
(1927) edition. MR
1424469